Augmented Variational Principles and Relative Conservation Laws in Classical Field Theory

Fatibene, L.; Ferraris, Maurizio; Francaviglia, M.

doi:10.1142/s0219887805000557

Cited by 31 publications

(83 citation statements)

References 16 publications

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“…These criticisms stress that the approach is by no means a covariant one (see for example [7,8]), or argue against any definition of energy in General Relativity referring to 3-surface integrals, instead of being quasi-local (referring to 2-surface integrals) from the very beginning [9], or even accept the approach for asymptotically flat space-times but express some doubts for the non asymptotically flat ones [10].…”

Section: General Considerationsmentioning

confidence: 99%

Intrinsic vanishing of energy and momenta in a universe

Lapiedra

Morales-Lladosa

2011

Gen Relativ Gravit

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We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in general relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular three-momenta vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lema{\^{\i}}tre-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.Comment: Enlarged and modified version, where several comments have been added (20 pages), of the previous manuscript: "Creatable universes: a new, and more consistent and general approach". In particular, changes involve a new title and updated references. Accepted in General Relativity and Gravitatio

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Section: General Considerationsmentioning

confidence: 99%

Intrinsic vanishing of energy and momenta in a universe

Lapiedra

Morales-Lladosa

2011

Gen Relativ Gravit

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“…Sometimes a group of spacetime transformations naturally induces a group of transformations on configurations (e.g., when configurations are represented in terms of spacetime tensors or more generally by geometrical objects) but in general it does not. From this viewpoint, Lie derivatives of fields with respect to spacetime vector fields is an additional (and not necessary) structure; one somehow needs to require naturality (17) while the lift (19) and its naturality (18) is not always available (nor, in fact, necessary).…”

Section: Noether Theoremmentioning

confidence: 99%

Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

2010

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Abstract:We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural Theories" that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincaré-Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as "generators of Noether symmetries", energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-called ADM laws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation "à la Palatini" and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero-Immirzi connections).

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“…Further energy conservation in a spacetime is guaranteed in the frame using a timelike KV to define the time direction. However, in the absence of a timelike KV the energy of a test particle is not defined and hence the energy in the gravitational field is not well defined (of course, one could use the quasilocal energy defined for a Lagrangian for a field theory using an ADM foliation see [2,3]). …”

Section: Introductionmentioning

confidence: 99%

Approximate Noether symmetries of the geodesic equations for the charged-Kerr spacetime and rescaling of energy

2009

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Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minkowski spacetime. First introducing spin angular momentum per unit mass as a small parameter we consider first-order approximate symmetries of the Kerr metric as a first perturbation of the Schwarzschild metric. We then consider the second-order approximate symmetries of the Kerr metric as a second perturbation of the Minkowski metric. The approximate symmetries are recovered for these spacetimes and there are no nontrivial approximate symmetries. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the charged-Kerr metric has to be rescaled and the rescaling factor is r -dependent. This re-scaling factor is compared with that for the Reissner-Nordström metric.

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Augmented Variational Principles and Relative Conservation Laws in Classical Field Theory

Cited by 31 publications

References 16 publications

Intrinsic vanishing of energy and momenta in a universe

Intrinsic vanishing of energy and momenta in a universe

Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

Approximate Noether symmetries of the geodesic equations for the charged-Kerr spacetime and rescaling of energy

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